# Relativistic rolling tank

Pete said:
Mac has brought up an interesting simultaneity issue.

There are two simultaneity issues in the scenario. Mac's issue is related to the tank getting up to speed. The other, which is related and easier to address first, is related to the tank cruising at constant velocity.

First issue
In the rolling tank's reference frame, there are the same number of cleats on the top section as on the bottom section.
But in the ground reference frame, the rolling tank has more cleats on the top section than the bottom.
How is this possible?

Second issue
In the ground reference frame, there are the same number of cleats on the top section as on the bottom section before the tank starts rolling.
But the rolling tank has more cleats on the top section than the bottom.
The driving wheels are both going at the same speed (as we know from the tank reference frame), and there is no slipping of the tread on the wheels (again, we know this from the tank frame), so how do the extra cleats get to the top section?
I think the question should be "why does anyone find this an issue at all?"
No1, The top of the track sees no more cleats than the bottom(if you caount up how many cleats that have past appeared on the top it would be equal to the bottom.
No2, The cleats on the top of the track will never travel the more distance than the cleats on the bottom wrt to a ground clock.
N03, Any teeth on the inside will mirror(or act the same as) the cleats so there would be no slippage.
No4, tHE bottom of the track is stretched x2 and the bottom of the track is stretched x 2(for reasons that I have tried to explain but I just cant at the moment), there is no concertinaing up on the top of the track compared to the bottom being overly stretched if you calculate correctly.

MacM said:
Do you really think that trying to shift the attentioon somehow changes the facts.

THE TANK TREADS ARE MECHANICALLY SYNCHRONIZED TO HAVE UNIFORM DISTRIBUTION OF CLEATS ACROSS THE UPPER AND LOWER SECTIONS.

THAT CANNOT CHANGE AS YOU HAS SHOWN IT UNLESS YOU HAVE THE TREAD SKIP TEETH ON THE COG IN ADDITTION TO DIFFERENTIAL CONTRACTION AS A FUNCTION OF OBSERVER VIEW.

SPEAKING OF WAVING HANDS.
Replying in all caps doesn't make you right. You know as well as I do that synchronization is relative in SR. The fact that they are synchronized in one frame to have uniform distribution does not imply that they are synchronized in another frame. If you want to make a claim of paradox, then support your claim with careful work, not all caps and repetition.

-Dale

DaleSpam said:
Replying in all caps doesn't make you right. You know as well as I do that synchronization is relative in SR. The fact that they are synchronized in one frame to have uniform distribution does not imply that they are synchronized in another frame. If you want to make a claim of paradox, then support your claim with careful work, not all caps and repetition.

-Dale

Right and you know as well as I that you can't apply your simultaniety to track engaged around the drive wheels in the same way that you do in linear transformation.

So don't try to avoid the issue by making comment about caps. Caps were to emphasize the issue for discussion not the predetermined merits of the arguement. So discuss the issue.

MacM said:
you can't apply your simultaniety to track engaged around the drive wheels in the same way that you do in linear transformation.
Why not? Try some actual work here.

It is well known that perfectly rigid bodies are not allowed in relativity. Deformable bodies can stretch or compress. Stretching or compressing certainly allows simultaneity to be frame dependent without requiring any "slippage". Therefore your claim is not at all clear, and you need to back it up with some careful work and not your usual hand waving.

-Dale

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DaleSpam said:
Why not? Try some actual work here.

It is well known that perfectly rigid bodies are not allowed in relativity. Deformable bodies can stretch or compress. Stretching or compressing certainly allows simultaneity to be frame dependent without requiring any "slippage". Therefore your claim is not at all clear, and you need to back it up with some careful work and not your usual hand waving.

-Dale

Absolute crap. Please indicate even in some cursory manner just how you can apply your "Deformable Bodies" escape goat to allow multiple cleats to escape the lower track and be past the drive cog and firmly in the upper track.

You are a joke. SR isn't. It is simply detrimentail to progress.

I think I read in a previous post that the cleats were not meant to be part of the tracks but were only reference marks. If the cleats were part of the track, there should be the same amount on top and bottom. The distortion would extend all the way to the most elemental particles of the track, seems to me.

Vern said:
I think I read in a previous post that the cleats were not meant to be part of the tracks but were only reference marks. If the cleats were part of the track,.
They could well be actual cleats and well be physically part of the track as well as just reference points.

MacM said:
Absolute crap. Please indicate even in some cursory manner just how you can apply your "Deformable Bodies" escape goat to allow multiple cleats to escape the lower track and be past the drive cog and firmly in the upper track.
Deformable bodies aren't necessary, except to allow the track to stretch.

The issue of cleats "migrating" to the upper track in the ground frame as the tank gets up to speed is related to the well known Bell's spaceship paradox. In the ground frame, the rear drivewheel turns faster than the front drivewheel while the tank is accelerating.

This in turn is due to relative simultaneity. At any instant in the tank frame, the drivewheels are going at the same speed. But in the ground frame, the front wheel lags behind during acceleration. For example, consider the time at which the two drive wheels reach 0.5c. In the tank frame, these events occur simultaneously... but in the ground frame, the rear event occurs first.

Note that this is the same mechanism that allows the rear wheel to catch up to the front wheel in the ground frame as the tank accelerates.

Relativity of simultaneity could also explain why the axels are measured as being half the distance apart in the ground frame. The distance between the rounded 'ends' of the track should also contract in the ground frame, along with the axels, as they are also moving at .866c in the ground frames. Relativity of simultaneity again. But the cleats, or measuring marks, on the bottom of the tread cannot be contracted in the ground frame as they are 'at rest' wrt the ground. No relativity of simultaneity can be applied to the measuring marks or cleats on the bottom as they are not moving wrt the ground.

There will be seven times as many cleats on the top of the track as on the bottom of the track in the ground frame. The cleats on top of the track will be 1/7 the distance apart as the cleats on the bottom, as measured from the ground frame.

The axels themselves correspond to the familiar 'relativistic cartwheel' in the gedankin. The 'cogs' on the axels are wider apart at the ground than they are after they have moved to the top of the axel. This explanation is consistent with Special Theory, I believe.

MacM said:
Absolute crap.
MacM, everyone knows you are the one who is full of absolute crap. I am only full of relative crap.

MacM said:
Please indicate even in some cursory manner just how you can apply your "Deformable Bodies" escape goat to allow multiple cleats to escape the lower track and be past the drive cog and firmly in the upper track.
There are three effects involved here that you need to consider. The first effect is the relativity of simultaneity. You seem to think that it doesn't apply for a mechanical system for some reason. Pete already outlined how it does. As the tank accelerates the front axle is deeper in the "acceleration well" so it runs slower and simultaneity is lost. This gives more treads on the top than on the bottom. The second effect is length contraction. The treads on the top are moving faster so they are Lorentz contracted and more treads fit on top than on bottom. The third effect is material deformation. The tank tread motion is not Born rigid, therefore there must be some strain in the treads and drive cogs as it goes to higher velocities.

Now, by claiming a paradox you are claiming that these three effects cannot possibly balance out into a self-consistent whole. That assertion is not at all apparent and needs some serious and careful supporting work. I know that I lack the math to even set up the calculation, so I am willing to place pretty high odds that you don't know how to do it either. Despite not even knowing how to set up the calculation you claim to know the result, this is intellectually dishonest. As usual, all you have here is your repetitive prejudice and bias against SR; you have no supporting logic or work, and it is definitely needed here.

-Dale

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DaleSpam said:
Now, by claiming a paradox you are claiming that these three effects cannot possibly balance out into a self-consistent whole. That assertion is not at all apparent and needs some serious and careful supporting work.
Is it really that complicated? If you describe your conveyorbelt or wheel, say by tracking the wordlines of all its constituent parts in one reference frame, you can use the Lorentz transformations to find the worldlines in any other frame. The worldlines are determined by certain laws in physics which predict how all the particles interact with one another, as well as the assumptions made about the initial properties (velocities, etc.) of these particles.

The way I see it, the issue is whether transforming the initial conditions and then applying the laws of physics in the primed frame would yield the same worldlines as making the predictions in the unprimed frame and then applying the transformation. In other words, it's simply a queston of whether or not the laws of physics remain invariant under a Lorentz transformation.

I think the laws of physics remain invariant. The transformation has to apply to the whole top of the tread as well as to the cleats on it. So, it still seems that there will be the same number of cleats on top as bottom.

przyk said:
Is it really that complicated? If you describe your conveyorbelt or wheel, say by tracking the wordlines of all its constituent parts in one reference frame, you can use the Lorentz transformations to find the worldlines in any other frame. The worldlines are determined by certain laws in physics which predict how all the particles interact with one another, as well as the assumptions made about the initial properties (velocities, etc.) of these particles.

The way I see it, the issue is whether transforming the initial conditions and then applying the laws of physics in the primed frame would yield the same worldlines as making the predictions in the unprimed frame and then applying the transformation. In other words, it's simply a queston of whether or not the laws of physics remain invariant under a Lorentz transformation.
I agree. If I were to try to set up this problem that is essentially how I would approach it. I would find an equation for the worldline of an arbitrary material point in the tank's reference frame and then Lorentz transform to and from the ground frame. If MacM really wants to show a paradox then what he would need to show is that Lorentz transforming gets some material point at two different locations in the same frame or two different strains or something similar.

-Dale

Vern said:
I think the laws of physics remain invariant. The transformation has to apply to the whole top of the tread as well as to the cleats on it. So, it still seems that there will be the same number of cleats on top as bottom.
You are forgetting the relativity of simultaneity. The number of cleats on top or bottom is specified at a particular time, and "a particular time" refers to a different sets of events in different frames. In other words, if you mark the number of cleats between two events then both frames will agree, but the two events will not be simultaneous in both frames.

-Dale

2inquisitive said:
Relativity of simultaneity could also explain why the axels are measured as being half the distance apart in the ground frame. The distance between the rounded 'ends' of the track should also contract in the ground frame, along with the axels, as they are also moving at .866c in the ground frames. Relativity of simultaneity again. But the cleats, or measuring marks, on the bottom of the tread cannot be contracted in the ground frame as they are 'at rest' wrt the ground. No relativity of simultaneity can be applied to the measuring marks or cleats on the bottom as they are not moving wrt the ground.

There will be seven times as many cleats on the top of the track as on the bottom of the track in the ground frame. The cleats on top of the track will be 1/7 the distance apart as the cleats on the bottom, as measured from the ground frame.

The axels themselves correspond to the familiar 'relativistic cartwheel' in the gedankin. The 'cogs' on the axels are wider apart at the ground than they are after they have moved to the top of the axel. This explanation is consistent with Special Theory, I believe.

I agree with you, 2inq.

DaleSpam said:
I agree. If I were to try to set up this problem that is essentially how I would approach it. I would find an equation for the worldline of an arbitrary material point in the tank's reference frame and then Lorentz transform to and from the ground frame. If MacM really wants to show a paradox then what he would need to show is that Lorentz transforming gets some material point at two different locations in the same frame or two different strains or something similar.

-Dale
My point was that all of this seems unnecessary. All MacM would need to do generally is show that one of the fundamental laws in physics was not Lorentz invariant (like martillo tried with the de Broglie formula). There's no way a relativity paradox can exist if all the laws are Lorentz invariant, so your bet would appear to be a safe one.

przyk said:
My point was that all of this seems unnecessary. All MacM would need to do generally is show that one of the fundamental laws in physics was not Lorentz invariant (like martillo tried with the de Broglie formula). There's no way a relativity paradox can exist if all the laws are Lorentz invariant, so your bet would appear to be a safe one.
Oh, I see what you are saying. Well, the relativistic formulation of Newton's laws are Lorentz invariant for general motions, so there is no way that the particular motion of a tank tread could make a paradox that way. I would guess that his best bet would be to look for inconsistencies in Hooke's law. I certainly haven't seen a relativistic formulation and I suspect that the standard formulation is probably not Lorentz invariant. Maybe MacM will have better luck with Hooke than martillo did with deBroglie. Of course, I don't think that Hooke's law would really qualify as a "fundamental law" any more than Ohm's law.

-Dale

Pete said:
I agree with you, 2inq.
What you agree that he has once again taken my point and asserted he originated it , I hate this tosser!

You pete also agree this is merely a gendanken? Jesus Christ the worlds gone mad.

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Ummmm, no... I agree with the facts as stated in the post that I replied to. I don't particularly care who originated what point - it's not a competition.

Pete said:
Ummmm, no... I agree with the facts as stated in the post that I replied to. I don't particularly care who originated what point - it's not a competition.
Well get it straight who brought the point up!
Also are you completely unaware that he is actually taking the piss out of you aswell as attempting to with me?